Clipboard erased when quitting Blender on Ubuntu
I posted a bug report on this, but apparently it's not Blender's fault.
As Sergey explained in the bug report, Blender only instructs the clipboard manager to save the text, but in Ubuntu, this is a bug that affects many programs.  You can read more about why it happens here.
Going to the Ubuntu Software Center and installing the application Parcellite, which is an alternative clipboard manager has fixed the problem for me.
EDIT: I also had some problems with Parcellite and Blender working together.  You could try a different clipboard manager.